摘要 : There is a longstanding conjecture by Froberg about the Hilbert series of the ring R/I, where R is a polynomial ring, and I an ideal generated by generic forms. We prove this conjecture true in the case when I is generated by a la... 展开 There is a longstanding conjecture by Froberg about the Hilbert series of the ring R/I, where R is a polynomial ring, and I an ideal generated by generic forms. We prove this conjecture true in the case when I is generated by a large number of forms, all of the same degree. We also conjecture that an ideal generated by m'th powers of generic forms of degree d2 gives the same Hilbert series as an ideal generated by generic forms of degree md. We verify this in several cases. This also gives a proof of the first conjecture in some new cases. 收起